Resonance graphs of catacondensed even ring systems are median (Q1613516)

The authors consider cers, which are planar graphs consisting of even ring systems whose inner dual is a tree. This class of graphs is of interest to chemical graph theory. Motivated by the resonance graph of Kekulé structures the authors introduce a resonance graph \(R(G)\) for a cers \(G\). The vertices of \(R(G)\) correspond to the 1-factors of \(G\). They are connected by an edge if their symmetric difference is the edge set of a bounded face of \(G\). The main result of the paper is that the resonance graph of a cers is a median graph.